В треугольнике со сторонами: a = 12.73, b = 49.2, с = 47.52, углы равны α° = 15°, β° = 90°, γ° = 75°
Ответ:
a=12.73
b=49.2
c=47.52
α°=15°
β°=90°
γ°=75°
S = 302.74
ha=47.56
hb=12.31
hc=12.74
P = 109.45
Решение:
Сторона:
c = b·
sin(γ°)
sin(β°)
= 49.2·
sin(75°)
sin(90°)
= 49.2·
0.9659
1
= 49.2·0.9659
= 47.52
Угол:
α° = 180 - γ° - β°
= 180 - 75° - 90°
= 15°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √49.22 + 47.522 - 2·49.2·47.52·cos(15°)
= √2420.6 + 2258.2 - 4676·0.9659
= √162.25
= 12.74
или:
a = b·
sin(α°)
sin(β°)
= 49.2·
sin(15°)
sin(90°)
= 49.2·
0.2588
1
= 49.2·0.2588
= 12.73
или:
a = c·
sin(α°)
sin(γ°)
= 47.52·
sin(15°)
sin(75°)
= 47.52·
0.2588
0.9659
= 47.52·0.2679
= 12.73
Периметр:
P = a + b + c
= 12.73 + 49.2 + 47.52
= 109.45
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√54.73·(54.73-12.73)·(54.73-49.2)·(54.73-47.52)
=√54.73 · 42 · 5.53 · 7.21
=√91650.562458
= 302.74
Высота :
ha =
2S
a
=
2 · 302.74
12.73
= 47.56
hb =
2S
b
=
2 · 302.74
49.2
= 12.31
hc =
2S
c
=
2 · 302.74
47.52
= 12.74